(a) Suppose we have the following production function: Q = 10 K + 5L. Confirm the...

 

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(a) Suppose we have the following production function: Q = 10 K + 5L. Confirm the technology is constant returns to scale (CRS). Show your work and explain what it means. (b) Suppose K and L are both variable. Letr = $20 and w= $20. What is the firm's cost minimization problem? Show and explain using the isocost and isoquants in a figure. Be sure to show their slopes. (c) Now derive the long-run cost function for r = $20 and w= $20. You can use math or a table to do this. (d) Confirm that average and marginal costs are constant. Explain why this is the case. (e) Now suppose r rises above $20. At what value ofr will the firm switch from K into L? Explain and use the isocost/isoquant to explain. (f) Show that long-run average costs rise as r rises (but stop rising if r is "very high"). Explain your reasoning. (g) What do we mean by an exit price? What is the exit price if r = $15. What is the exit price ifr = $60? Explain. (a) Suppose we have the following production function: Q = 10 K + 5L. Confirm the technology is constant returns to scale (CRS). Show your work and explain what it means. (b) Suppose K and L are both variable. Letr = $20 and w= $20. What is the firm's cost minimization problem? Show and explain using the isocost and isoquants in a figure. Be sure to show their slopes. (c) Now derive the long-run cost function for r = $20 and w= $20. You can use math or a table to do this. (d) Confirm that average and marginal costs are constant. Explain why this is the case. (e) Now suppose r rises above $20. At what value ofr will the firm switch from K into L? Explain and use the isocost/isoquant to explain. (f) Show that long-run average costs rise as r rises (but stop rising if r is "very high"). Explain your reasoning. (g) What do we mean by an exit price? What is the exit price if r = $15. What is the exit price ifr = $60? Explain.

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Answer a We can confirm that the technology is constant returns to scale by taking different values for K and L and seeing if the output Q changes in proportion For example if we take K 2 and L 1 then ... View the full answer