1. (20 points) [VF] A firm is using a Cobb-Douglas production function q = (K(a)) (L(1a)) in

the creation of bottled soda. Let q = the number of cases of bottled sodas, K = the number of

machines, L = the number of workers hired, and a = 13

.

(a) (2 points) [VF] Suppose that the firm only has access to K = 25 machines currently. If the

current market price for a case is P = $36?, the rental rate of captial r = $24?, and wage

rate is w; then, find the optimal choice of L the firm should hire (hint: choice will be a

function of w)?

(b) (3 points) [VF] In the town, the labour supply is inelastic in the short-run with LS = 1, 600.

What would happen if the government set a minimum wage of w = f$10, $12, $15g (hint:

think how many would be hired versus how many would want to work for each of the 3

wages and number may have a decimal point)?

(c) (4 points) [VF] Suppose the market wage is w = $6 based on LS = 1, 600 which means

the firm would produce q = 400 cases in the short-run. If the firm continues to produce

q = 400 and is able to adjust K and L (with P = $36, w = $6, and r = $24), how many

people would be hired and how much capital would be used (note: assume the labour

supply LS will have time to adjust and is not fixed).

(d) (6 points) [VF] How do the short-run profits from part (c) compare with the outcome

when the firm can adjust K and L? Use a sketch to explain why this would be the case

(make sure to label your sketch).

(e) (5 points) [VF] Suppose a new technology comes along allowing the firm to replace all

their existing machines resulting in production of q = z (K(a)) (L(1a)) where z > 1

or the firm can introduce a new method with the existing machinary making production

q = (K(a)) (zL)(1a) for z > 1, i.e. there is a neutral technological change or a labour

saving change in the method of production. Which technology would the firm prefer?

(hint: if stuck try z = 27) How should the firm respond in the short-run? Is your answer

the same for the long-run? Explain.