Question

The (short-run) production function for ACME Widgets is given byQ= 50K0(L−10)2/3, where Q is the weekly output of widgets, L is the weekly labor input,measured in $1000s, and K0 is the fixed level of capital input.

a. Compute the labor-elasticity of output, ηQ/L, as a function of L.

b. What is the labor-elasticity of output when labor input is $45000 a week?

c. Suppose that ACME hires two additional widget polishers, at a combined cost of $1500 a week. Use your answer to part b. to estimate the resulting percentage change in output.

d. Can the answers above be used to estimate the change in ACME’s weekly revenue? If so, what is the resulting change in revenue? If not, explain why not.

Answer 1

A:- a. Compute the labor-elasticity of output, η_Q/L, as a function of L

η_Q/L =( dQ /dL)*( L/ Q) = (2/3)* 50K₀(L − 10)^−1/3 *L/( 50K₀(L − 10)^2/3) = 2L /3(L − 10).

B:- What is the labor-elasticity of output when labor input is $45000 a week?

η_Q/L L where L=45 = 90 /105 = 6 /7 .

C:- Suppose that ACME hires two additional widget polishers, at a combined cost of $1500 a week. Use your answer to part b. to estimate the resulting percentage change in output.

This can be accomplished with the help of approximation formula %∆Q ≈ η_Q/L(%∆L).

First, compute the percentage change in labor input,

%∆L = (∆L /L_old )· 100% ≈ 3.33%.

Thus,

%∆Q ≈ (6/ 7) · 3.33% ≈ 2.85%.

D:- Can the answers above be used to estimate the change in ACME’s weekly revenue? If so, what is the resulting change in revenue? If not, explain why not

No, the main logic behind this is that the price and output of the widget will decide the total revenue. The demand of the widget is not f=reflected by the production function so there is no help with the price or the revenue

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