Suppose that the following production finetion is given: Q==D4KLFor the above production function, find the elasticity of substitution? Find the Retams to Scale.Using the above production funetion: find the labor demand and capital demand as functions of output(Q). price of labor (w) and price of capital (r). Does the Law of Demand hold for each inpur? Are these inputs normalor infenior inputs in the production process? Are inputs complements or substitutes? Why?Find the cost function for the above production finction. Verify the properties of the cost function.Suppose that a fim wants to produce 144 units of output and w-1, r-l. Find long run total cost.Suppose now that wage goes up to 4. Find the new long run total cost. Does fim substitute capital for labor? Whatis the percentage of cost saving relative to the case where firm is not able to substitute?Suppose that w=1, r-1 and a fimm has fixed amount of capital K 16 in short nun (SR). Find theshort run total cost, average total cost and marginal cost. What would be the short run total cost of producing 144units. Compare your answer with long nun total cost in part d. How and why are they different?

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Suppose that the following production fnction is given: Q-4KL For the above production function, find the elasticity of substitution? Find the Retuns to Scale.

ENGR.ECONOMIC ANALYSIS

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Chapter1: Making Economics Decisions

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Question

Suppose that the following production finetion is given: Q=
=D4KL
For the above production function, find the elasticity of substitution? Find the Retams to Scale.
Using the above production funetion: find the labor demand and capital demand as functions of output
(Q). price of labor (w) and price of capital (r). Does the Law of Demand hold for each inpur? Are these inputs normal
or infenior inputs in the production process? Are inputs complements or substitutes? Why?
Find the cost function for the above production finction. Verify the properties of the cost function.
Suppose that a fim wants to produce 144 units of output and w-1, r-l. Find long run total cost.
Suppose now that wage goes up to 4. Find the new long run total cost. Does fim substitute capital for labor? What
is the percentage of cost saving relative to the case where firm is not able to substitute?
Suppose that w=1, r-1 and a fimm has fixed amount of capital K 16 in short nun (SR). Find the
short run total cost, average total cost and marginal cost. What would be the short run total cost of producing 144
units. Compare your answer with long nun total cost in part d. How and why are they different?

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.2. Tiva has a crafts store that makes jewelry using beads (B) and copper (C). Her productionfunction for jewelry is given byQ = B0.4C0.4Suppose she can buy beads and copper at prices PB and PC, respectively.(a) Calculate Tiva’s marginal rate of technical substitution between B and C.(b) Does this production function have increasing, constant, or decreasing returns to scale?Explain. (c) Set up the cost minimization problem you would use to calculate Tiva’s cost functionC(Q) in Lagrangian form. (Note: You do not need to solve it or derive first orderconditions.Suppose Tiva decides to branch out in her jewelry offerings by getting a 3D printer. The costof producing new 3D printed jewelry isC(Q) = 25 + Q24For the rest of this problem, assume Tiva can produce fractions of jewelry, don’t worry aboutrestricting your answers to whole numbers.(d) Compute Tiva’s marginal cost and average cost of production for 3d printed jewelry.(e) Explain why she will shut down when the market price falls…
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