Question

Answer part (A) please

1. Short Run Cost Curves: Consider two firms, producing different products, with the following production functions: (1) q-5KL q=5(KL)5 (2) a. For a short-run situation in which K=100, and given wage 3 and cost of capital 1, derive expressions short run total cost for each production function. (Start by using the production function to develop an expression for L in terms of q, and then substitute that, and the given parameters, into the generic expression for Total Cost wL+ yK to get cost as a function of q.) Also derive the short run average cost and short run marginal cost curves for both functions (with cost as a function of q in each case). (10) b. Plot each short-run total cost curve on a separate graph of cost (on the vertical axis) vs. q (on the horizontal axis). Label these curves "TC1." Now suppose (for each case) that the cost of capital goes up to 2. (Continue to assume we're in the short run and K can not be altered). How would this change alter your total cost curve? Plot these curves and label them "TC2."(5) c. Finally, beginning from your original TC1 curve, suppose that wages fall to 2. How would this alter your TC curve? Plot these new curves and label them "TC3" in each case. (5)

Answer 1

a. Firm one and two's production functions in the short run transform to:
$\dpi{80} \fn_phv \small q_1=500L, q_2=50\sqrt{L}$

Using these production functions, amount of labor employed by these firms in the short run is:
$\dpi{80} \fn_phv \small L_1=\frac{q_1}{500}, L_2=(\frac{q_2}{50})^2$

The cost function for firm one is:
$\dpi{80} \fn_phv \small C_1=3L_1+K_1=\frac{3q_1}{500}+100$

The average and marginal cost functions are:
$\dpi{80} \fn_phv \small AC_1=\frac{3}{500}+\frac{100}{q_1}, MC_1=\frac{3}{500}$

The cost function for firm two is:
$\dpi{80} \fn_phv \small C_2=3L_2+K_2=3*(\frac{q_2}{50})^2+100$
The average and marginal cost functions are:
$\dpi{80} \fn_phv \small AC_2=\frac{3q_2}{(50)^2}+\frac{100}{q_2}, MC_2=\frac{6q_2}{50}$