Lecture 3 - The Long Run Model of Production and Supply

Question 1

Define the Marginal Product of Labour (MPL) and the Marginal Product of Capital (MPK)

Answer 1

the amount of extra output produced when labour/capital increases by one unit

Question 2

What are the equations for MPL and MPK?

Answer 2

• MPL = F(K, L+1) - F(K,L)
• MPL = (dF(K,L))/dL
• MPK = F(K+1, L) - F(K,L)
• MPK = (dF(K,L))/dK

Question 3

For the neoclassical production function, what is the assumption about returns to scale?

Answer 3

that there are constant returns to scale

Question 4

When looking at this very simple economy, what are the 3 assumptions about the openness of the economy, the number of goods consumed/produced, and how markets and prices behave?

Answer 4

• single, closed economy
• one good is consumed/produced
• markets clear and prices are flexible

Question 5

For the neoclassical production function, what is the assumption about marginal returns?

Answer 5

that there are diminishing marginal returns

Question 6

What is meant by diminishing marginal returns?

Answer 6

as only one factor is increased, its marginal product decreases (other things equal)

Question 7

What is the Cobb-Douglas production function? What does it show in relation to returns to scale and MPL & MPK?

Answer 7

• Y = A(K^α)(L^(1-α)), 0<α<1
• constant returns to scale
• MPL and MPK are positive, but are diminishing in L,K

Question 8

In this model, what do we assume in terms of the supply of factors of production?

Answer 8

capital (K) and labour (L) are assumed to be in fixed supply

Question 9

How do you show that something is in fixed supply when you write it?

Answer 9

a horizontal line above the letter

Question 10

Firms hire workers at wage W, and sell output at price P; derive how MPL = W/P for firms’ demanding labour

Answer 10

• ∆profit = ∆revenue - ∆cost
• ∆profit = (P x MPL) - W
• keep hiring until ∆profit = 0
• 0 = (P x MPL) - W
• MPL = W/P

Question 11

Firms rent capital at rate R, and sell output at price P; derive how MPK = R/P for firms’ demanding labour

Answer 11

• ∆profit = ∆revenue - ∆cost
• ∆profit = (P x MPK) - R
• keep hiring until ∆profit = 0
• 0 = (P x MPK) - R
• MPL = R/P

Question 12

What is the equation for economic profit?

Answer 12

economic profit = Y - (MPL x L) - (MPK x K)

Question 13

Because of Euler’s theorem, if F has CRS, then Y = F(K,L) = ?

Answer 13

Y = F(K,L) = (MPL x L) + (MPK x K)

Question 14

What is the equation for accounting profit?

Answer 14

accounting profit = economic profit + (MPK x K)

Question 15

For the production model, output per person in equilibrium is the product of which two key forces ?

Answer 15

• productivity, A (aka ‘total factor productivity’, TFP)
• capital per person, k

Question 16

What do we assume about firms in this production model?

Answer 16

• firms have demand for capital and labour as inputs of production
• firms are perfectly competitive (small, price takers, profit maximisers…)

Question 17

What are the 5 exogenous variables in this model?

Answer 17

• output (Y)
• amount of capital (K)
• amount of labour (L)
• real wage (W/P)
• real rental rate of capital (R/P)

Question 18

What are the 5 equations in this model?

Answer 18

• the production function
• the rule for hiring capital
• the rule for hiring labour
• supply = demand for capital
• supply = demand for labour

Question 19

What are the parameters in this model?

Answer 19

• the productivity parameter, A
• the exogenous supplies of capital and labour
• the production function parameter α