Q3: (10 points) LONG-RUN COSTS and OPTIMIZATION: Consider a firm that employs capital (K) and labour (L) and uses the p
Posted: Thu Jun 09, 2022 4:28 pm
Q3: (10 points) LONG-RUN
COSTS and OPTIMIZATION: Consider a firm that employs
capital (K) and labour (L) and uses the production technology
Q = 3K + 4L. Let factor prices be r = $40
for capital and w = $20 for labour.
f) Suppose P falls to $1.8. Confirm that the firm will choose Q=0 (eg shut-down). Explain what is happens. 02: (10 points) SHORT-RUN COSTS and OPTIMIZATION: Consider the following production function: Q=K3L43. Let the price of output be P = $100 and factor prices w=$5 and r = $10. a) Assume that K is fixed at 64. What are the short-run costs? C-wl+d64)?. b) Plot cost versus output. Show that costs are accelerating. Why is this the case? (hint. What are the returns to scale?) c) What is the firm's optimization problem? d) What is the supply function for this firm? Eg, what is the relationship between market prices and the firm's optimal choice of output. Hint: look at MC = P. Confirm that higher P leads to higher Q. e) Graph the supply curve. Discuss its shape (eg why does the slope increase?). Q3: (10 points) LONG-RUN COSTS and OPTIMIZATION: Consider a firm that employs capital (K) and labour (L) and uses the production technology Q=3K+ 4L. Let factor prices be r = $40 for capital and w = $20 for labour. I a) What is the firm's minimization problem? b) Plot the isoquant for Q-100. What is the Marginal Rate of Technical Substitution (MRTS)? c) For any output Q, what is the optimal combination of K and L given the input prices? Hint set MRTS = r/w and solve for L) d) What is the cost function? Confirm C(Q-100) = 500 e) Given the above, what must the supply curve look like in long-run equilibrium? TOTAL: 20 points
COSTS and OPTIMIZATION: Consider a firm that employs
capital (K) and labour (L) and uses the production technology
Q = 3K + 4L. Let factor prices be r = $40
for capital and w = $20 for labour.
f) Suppose P falls to $1.8. Confirm that the firm will choose Q=0 (eg shut-down). Explain what is happens. 02: (10 points) SHORT-RUN COSTS and OPTIMIZATION: Consider the following production function: Q=K3L43. Let the price of output be P = $100 and factor prices w=$5 and r = $10. a) Assume that K is fixed at 64. What are the short-run costs? C-wl+d64)?. b) Plot cost versus output. Show that costs are accelerating. Why is this the case? (hint. What are the returns to scale?) c) What is the firm's optimization problem? d) What is the supply function for this firm? Eg, what is the relationship between market prices and the firm's optimal choice of output. Hint: look at MC = P. Confirm that higher P leads to higher Q. e) Graph the supply curve. Discuss its shape (eg why does the slope increase?). Q3: (10 points) LONG-RUN COSTS and OPTIMIZATION: Consider a firm that employs capital (K) and labour (L) and uses the production technology Q=3K+ 4L. Let factor prices be r = $40 for capital and w = $20 for labour. I a) What is the firm's minimization problem? b) Plot the isoquant for Q-100. What is the Marginal Rate of Technical Substitution (MRTS)? c) For any output Q, what is the optimal combination of K and L given the input prices? Hint set MRTS = r/w and solve for L) d) What is the cost function? Confirm C(Q-100) = 500 e) Given the above, what must the supply curve look like in long-run equilibrium? TOTAL: 20 points