Economic Methods Part 1 Flashcards
What is excess supply and demand?
The difference between the amount of units demanded and the amount of units supplied when goods are at a certain price, 0 in equilibrium, created by government interference in market
What is important about tax collection?
It must be higher than tax revenue
Where Qs = a + BP, what is the supply function post-tax and post-subsidy?
Qs(t) = a + B(P-t) and Qs(k)= a + B(P+k)
Where Pd = a-BQd, what is the reverse demand function post-tax?
Pd-t = a-BQd
What is the rule with taxation and subsidisation in demand and supply functions?
The transformation always occurs in the price
What is the consumer share of tax imposed?
P**-P*, or the post-tax equilibrium price - the pre-tax equilibrium price
What is the percentage consumer share?
(P**-P*)/t x 100
What is the producers’ share of tax imposed and percentage share?
£t - (P**-P*) = M or share
M/t x 100 = percentage share
What is the secondary method of taxation?
Through the total revenue, where firms pay a tax tpq, or a percentage tax multiplied by their total revenue (pq)
What is the calculation for tax revenue?
Qt x t
What is Pc and Ps
The price consumers will pay and the price suppliers will pay
Capital and Labour: Substitutes?
They can be in certain circumstances so straight line on graph, other times not
What is the Cobb-Douglas production function?
AK^aL^b with A being technology, a the proportion of whole capital put into the single product being viewed on the graph, b is the same but for labour
What is the relationship between a and b and returns to scale?
(a+b) > 1 : increasing returns to scale
(a+b) < 1 : decreasing returns to scale
(a+b) = 1 : constant returns to scale
What does MC equate to in terms of cost and output?
Change in total cost/change in output
What is the break even point?
MR (Q) = MC (Q), or where TR = TC
What was the belief in macroeconomics before Keynes?
Assumption that demand will create itself as supply is increased, but stagflation of Great Depression dispelled this idea
Equation for closed economy
Supply : Y = C + I(r) + G = P(L, K) : Demand
What is the relationship between interest rates and investment?
Inversely proportional, the lower the interest rate, the higher the level of investment
Which formula’s allow the government to influence consumption C?
C = f(Yd), a function of disposable income Yd = Y - t C = a + bYd where a is autonomous consumption coming from private savings or borrowing and b is induced consumption, affected by income, creating bYd =MPC
What is the formula for b or MPC?
Change in consumption / change in Y
What is the formula for MPS based off of savings function?
(1-b)Y
What is the function for national savings?
Sn (national savings) = Sp (private savings) + Sg (government savings)
What are the two methods for measuring national income equilibrium?
Keynesian Cross and by use of savings and investment
How does the Keynesian cross work?
Where Y = AD and AD = C + I + G cross, there is equilibrium. Above this point AD < Y so a tax break should be brought in, where AD > Y, increase taxes
How do savings and investment measurements of national income equilibrium work?
As S = I, and I is set as an exogenous variable against
S = -a + (1-b)Y, where these two lines cross, that is the equilibrium point, so therefore interest rates can be adjusted so savings equal investment
How does government affect savings and investment graphs?
S + T = I + G
What is the formula for an open economy?
Y = C + I + G + NX(e) where e is the exchange rate, strong net importers have strong exchange
What is Young’s Theorem?
d²y/dwdx = d²y/dxdw
Where y = f(z, t), what is change in y?
Change in y or dy = (dy/dz) x dz + (dy/dt) x dt, so dy can be found when figures for z, t, dz and dt are given
What is the result of positive and negative FOCs?
Positive - increasing function
Negative - decreasing function
What is the result of positive and negative SOCs?
Positive - increasing rate of change - convex, often consumers desiring more of an item in U-shaped graph
Negative - decreasing rate of change - concave, item not desired by consumers
When z = f(x, y), how can a maximum and minimum b found?
d²z/dx² < 0 and d²z/dy² < 0 for maximum, reverse for minimum, in both cases d²zd²z/dx²dy² - (d²z/dxdy)² > 0 according to Young’s Theorem, where less than zero, no maximum or minimum, saddle point therefore
Formula for PED
Percentage change in Qd/percentage change in P or
dQd/dP x P/Qd so that by having a demand function and price P, PED can be solved
What do different sizes of the absolute value of n mean for price sensitivity?
|n| > 1 : elastic, price sensitive
|n| < 1 : inelastic, less price sensitive
|n| = 1 : unitary demand elasticity, change in Q = change in P
|n| = infinity perfectly elastic demand
|n| = 0 perfectly inelastic demand
How does elasticity affect TR when price is increased?
Inelastic: increase in price leads to increase in TR
Elastic: increase in price leads to decrease in TR
MR in terms of elasticity
MR = P + Q(dP/dQ) and PED = dQ/dP x P/Q rearranged and substituted so MR = P( 1 + 1/e)
What are the formulas for income demand of elasticity?
Percentage change in Qd/Percentage change in Y = YED
YED = dQd/dY x Y/Qd
How does the size of YED affect the value of goods?
YED > 1 : luxury good
YED < 1 : normal good
YED < 0 : inferior good
Formula for cross-price elasticity of demand
CPED = Percentage change in Qa/Percentage change in Pb CPED = dQa/dPb x Pb/Qa
How is substitutability affected by CPED?
CPED > 0 : substitutes
CPED < 0 : complements
CPED = 0 : no relationship
What is the formula for MU where TU = f(x, y)?
MU = dTU(x, y)/dx MU = dTU(x, y)/dy
What is the important thing about utility on the indifference curve?
It stays the same, so du = 0
Where U = f(x, y), what is the marginal rate of substitution?
|dy/dx| = -f ‘(x)/f ‘(y) = (dU/dx)/(dU/dy) = MRS
Formula for MPL and MPK in short and long run
MPL = dTP(Q)/dL in short run MPL = dTP(L, K)/dL in long run MPK = dTP(L, K)/dK in long run
How can indifference curves be described?
Isoquants
What is the marginal rate of technical substitution?
MRTS = dK/dL = MPL/MPK, rate at which labour can be substituted for capital to create the same amount of production
How does production change in the short run as inputs increase?
Returns to variable inputs or law of diminishing returns, MRTS falls to 0 as extra workers do not increase output
How does production change in the long run as inputs increase?
Returns to scale (powers of Cobb-Douglas function summed, a+b), or law of diminishing marginal returns
Q = AK^aL^b
d²Q/dL² > 0 - new labour is increasing production
d²Q/dL < 0 - new labour is not increasing production
Can be used for capital as well
What can the SOC show in a production function in terms of returns?
d²Q/dL² > 0 - increasing marginal returns
d²Q/dL² < 0 - decreasing marginal returns
What is a homogenous function?
A factor which can be built into another function without changing it
What is the production elasticity function for labour and capital?
Relative change in output relative to the percentage change in input, superscript a and b in a Cobb-Douglas Production Function
E(L): dQ/dL x L/Q where capital is held constant
E(K): dQ/dK x K/Q where labour is held constant
How can you explain MPS = 1 - MPC
Y = C + S dY/dY = dC/dY + dS/dY 1 = MPC + MPS
Basic formula for multiplier effect
1/(1-MPC) = 1/MPS or Change in real GDP (Y)/Change in injections (J)
When is output maximized in the short run?
Marginal product of labour = average product of labour, and also value of L when dAP(L)/dL = 0
How can revenue be maximised in perfect competition?
Price is constant, P = MR = AR, so it cannot really be maximised
How do you minimize costs in the short run?
Where ATC = MC or where dATC/dQ = 0
What area shows profits maximized in the short run on a graph?
Profits bound by the y-axis, Q, the minimum of the ATC and horizontal line MR = MC
What formula shows profits maximized?
Profit = TR - TC, then differentiate, equate to 0, test SOC
How to maximize profits in a multi-product firm with price discrimination?
Create separate profit functions using TR and TC, then find FOCs of these equal to 0, then SOCs
What does MR equate to in terms of elasticity and why is this useful in multi-product firms?
P(1 + 1/n) which can help show how where there is higher elasticity one market than another, there are lower prices
What are the two cases in constrained utility maximisation?
Primal case - maximising the utility curve given a certain budget constraint
Duality case - given a certain utility, the minimisation of expenditure to reach the curve
What is the point which is aimed for in a constrained utility maximisation case?
MUx/MUy = Px/Py
What is the objective function in a constrained optimisation case?
That which we set out to maximise or minimise
What is the producer duality case trying to achieve?
Cheapest (using budget line) way for firms to reach a certain output (constraint)
How does the substitution method work?
Substitute the objective function into the constraint so that one of the variables is isolated, then differentiate once for FOC, and again for SOC
Where the constraint is given by g(x, y) = m, what does the value of λ* show as m is increased or decreased (to be found in a langrangian equation)?
λ* > 0 and +1 unit change in M = increase approximately by λ*
λ* > 0 and -1 unit change in M = decrease approximately by λ*
λ* < 0 and +1 unit change in M = decrease approximately by λ*
λ* < 0 and -1 unit change in M = increase approximately by λ*
What is the budget constraint in a production case?
wL + rK = c = P(L)L + P(k)K
What is the primary point of optimisation in a production case?
|dL/dK| = r/w
What is the alternative point of optimisation in a production case?
P(L)/P(k) = MPL/MPK
In cases of integrating marginal revenue and costs to find totals, when is there a constant?
No constant in revenue to add on as when TR = 0, Q = 0. In marginal costs, the fixed cost is the constant which should be added to the integral of marginal costs
In cases of integrating marginal utility and marginal production, when is there a constant?
There is no constant in either case - for marginal utility, some utility is required for there to be a total, and for production, where there is no labour (or no capital), even with the other present, there is no output
How is integration used in macroeconomics in terms of savings and consumption and what are the constants?
Integral of MPS and MPC are savings and consumption functions, with T (non-income savings) added to savings function and K (autonomous consumption) added to consumption function
What are examples of flow (or rate, the derivative) in economics?
Deposits with interest and withdrawals, buying and selling shares, and housing stock
What are examples of stock (or capital, the integral) in economics?
Bank balance, housing investments and depreciation, equity shareholdings
What is the equation for net investment in terms of capital stock formation?
I(t) = dK(t)/dt
When net investment is integrated to find capital, what is the constant?
c = Ko = initial capital stock
What is the use of integration in economics?
Derive marginal functions, find the investment time path, create welfare measurements
Where exactly is the consumer surplus and producer surplus?
CS - area below demand curve but above equilibrium price
PS - area above supply curve but below equilibrium price
What is the use of total surplus?
To compare with other markets or the same market across time
How is the producer surplus found from the marginal cost function?
Where p = Po = output price for producing q = qo = maximising output, Po = MC (qo), therefore:
PS = Poqo - integral (qo to 0) of MC(q)
What are causes within countries of income and wealth inequality?
Ownership of resources, qualification, motivation, skill, ability, family size
What are causes across countries of income and wealth inequality?
Factor endowments, size and quality of labour force, good policy, luck, economic power, intuition
Main determinants are education and parental influence
How does inequality change as wealth and income increases?
First inequality increases, then decreases in U-shaped curve
What are the 3 popular measures of inequality?
Range ratios, Gini coefficient and Lorenz curve
How does the Lorenz curve work?
Income = population line drawn on graph with same axis, then a countries wealth distribution that falls below that line is drawn on - the area between the two lines is income inequality
Over which figures does the Gini coefficient result in?
0 < x < 1 with 0 being no income equality
What is the formula for the Gini coefficient?
2 (integral max: 1 min: 0 (x - f(x)) dx) where x is the equitable line and f(x) = L(x) or the inequality line a nation
What is the transpose of a matrix?
Amxn = A1 = AT = Anxm, swapping of the matrix order
What is an identity matrix?
Principle diagonal is 1 whilst all other values are 0
Which types of matrices can be summed?
Those with the same matrix dimension/order
What is scalar multiplication of a matrix?
Where a value multiplies the entire matrix such as 0.5A which causes all values of the matrix to be halved
What is the conformability rule for non-scalar multiplication?
Amxn x Bnxk = Cmxk, and as a result the order in which variables are multiplied is important
What does the determinant of a matrix show in terms of its relation to 0?
If |A| = 0 then the inverse of A does not exist, otherwise it does
What are the three steps in finding a 3x3 matrix determinant?
Find the minors, find the cofactors, and then evaluate the cofactors
What is the minor?
a11 x |a11| + a12 x |a12| + a13 x |a13|
What is a cofactor matrix?
One where every element (amxn) is replaced with its cofactor with an appropriate sign
What is an adjoint matrix?
A transposed cofactor matrix
What is the inversion of a matrix?
A^-1 = 1/|A| x AdjA
What happens to a 2x2 matrix when an inversion occurs?
The value of all elements are swapped diagonally
How is the Inversion Approach used?
AX = B rearranged to X = A^-1 x B where the inversion of the matrix is found and multiplied by B
How is the Cramer’s Rule Approach used?
Create alternative matrices (where differing columns of A is replaced by B), the determinants of these matrices are found and then these are divided by the original determinants
Xi = |Ai| / |A|
How does investment change from a Keynesian to Freidman’s model?
As money is important in impacting interest rates, creating I(r), investment is no longer exogenous
What are the three demands for money?
Transaction motive - Mt
Precautionary motive - Mg
Speculative motive - Mz
Equalling Ms when totalled
How does Y and r affect demand for money?
f(Y+) for Lt and Lp - more money required in a better economy
f(r-) for Lz - increase in interest rates lowers demand for speculative money
How is the SOC found in unconstrained optimization using the Hessian in terms of results?
Maximum or d²z < 0 when |H1| < 0, |H2| > 0 and |H3|<0, therefore negative definite
Minimum or d²z > 0 when |H1| > 0, |H2| > 0 and |H3| >0, therefore positive definite
How is Young’s Theorem applicable in the case of Hessians?
(Txx x Tyy) - (Txy)² > 0 should always been the case in 2x2 cases
What is the border made up of on the bordered Hessian?
The derivative of the constraint, such as gx and gy where gx is placed nearest Lxx
How are the results of a bordered Hessian SOC test found?
Where the result is positive, the result is a negative definite and is a maximum
Where the result is negative, the result is a positive definite and is a minimum
Use of the whole matrix |H| is required for evaluations to be made
