Provide a Total Cost Curve Diagram to sketch the long-run total cost C = C(q, w, r) and short-run total

A firm that is operating with production function q = K0.25L0.25 has mrts = K/L

A firm that is operating with production function q = K0.25L0.25 has mrts = K/L

Question
1) A firm that is operating with production function q = K0
.25L0
.25 has mrts = K/L and hires labour for w = 1
.00 and capital for r = 0
.25
.

a) Construct an Isoquant Diagram to illustrate how this cost minimizing firm would produce q = 2 units of output as bundle “a”, how the firm would implement a short-run increase in output to q = 4 units when capital is fixed at the level chosen for q = 2 as bundle “b” and how this firm would implement a long-run increase in output to q = 4 when capital in not fixed as bundle “c”

b) Provide a Total Cost Curve Diagram to sketch the long-run total cost C = C(q, w, r) and short-run total cost SC = SC(q, K, w, v) curves at q = 0, q = 2, and q = 4
.

c) Underneath the total cost curve diagram provide and Average Cost Curve Diagram to sketch the long-run AC curve and the short-run SATC, SAVC and SAFC curves at q = 0, q = 2, and q = 4
.

2) Is it alright doing two more, and I’ll pay extra?

In a competitive industry each firm has total costs C = q2 + 16
. Demand is D = 80 – 5p
. A $4 per-unit subsidy is introduced for this good
. Provide a pair of fully labeled diagrams showing “The Firm” and “The Industry” to outline the response to this subsidy
.

3) A perfectly competitive industry has many identical firms with total cost curves C = q2 + 16
. Market demand is given by D = 100 ? 5p
. Beginning next year the government will provide lump-sum tax of $9
.00 to all firms in this industry
. Provide a pair of fully labeled diagrams showing the firm and the industry along with supplemental calculations to assess the immediate response (before entry/exit) and ultimate response (after entry/exit) from this tax
.

A firm that is operating with production function q = K0.25L0.25 has mrts = K/L

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