Question

1a. The production function for computers is q(K,L) = 7K1/3L2 where K=capital and L=labor. A firm has two units of capital (K=2) which it cannot change. A manager wants to know the marginal productivity of labor if the firm goes from 2 to 3 workers. Calculate the marginal productivity of labor for the manager. Explain your answer carefully to the manager who is not familiar with what the marginal productivity of labor means.

1b. Last year the price of bread was $2.26 and Jen bought 4 loafs of bread. This year the price of bread is $2.57 and Jen bought 3 loafs of bread. Calculate the price elasticity of demand for bread. Explain your answer to the bread delivery person.

1c. Explain why in the short run a firm may not be able to change its inputs.

Answer 1

Please give ratings it will be appreciable, for any query please comment, Thank you

Solution 1a).

Production Function = 7K1/3L2

if K=2 is fixed q(K,L) = 7(2)1/3(L)2

q(K,L) = 7(1.26)(L)2 = 8.82(L)2

Marginal productivity is equal to an additional charge in the output due to additional changes in the input.

Marginal Productivity of labor = Change in the Output/ Change in Price

when Labour = 2

q=8.82(2)2 = 35.28

when Labour =3

q=8.82(3)2 = 8.82(9) = 79.37

Change in Output = 79.37 - 35.28 = 44.09

Chage in labour = 3 - 2 = 1

Marginal Productivity of labor = 44.09 / 1 = 44.09\

Solution 1b).

P1 = 2.26, P2 = 2.57

Q1 = 4, Q2 = 3

Change in quantity = Q2 - Q1 = 3 - 4 = -1

Change in Price = P2 - P1 = 2.57 - 2.26 = 0.31

the increase of a $1 unit of the price will decrease the loaf of bread by 2.76 units.

Solution 1c).

In a Short-Run,

we can't change the size of the plant and machinery used in the production in the short-run, hence, the raw material input also cannot be changed. Hence, firm cannot change its input in short-run.