# cost minimization

13. Suppose a worker is offered a wage of $10 per hour, plus a fixed payment of $120 per day, and he can use 24 hours per day. What is the market rate of substitution between leisure and income?

a) $5.

b) $8.

c) $10.

d) none of the above.

14. A perfectly competitive firm faces:

a) a perfectly elastic demand function.

b) a perfectly inelastic demand function.

c) a demand function with unitary elasticity.

d) none of the above.

15. For the cost function C(Q) = 100 + 2Q + 2Q^2, the total variable cost of producing 2 units of output is

a) 16.

b) 12.

c) 4.

d) none of the above.

16. Solutions to the principal-agent problem are intended to ensure that the firm is operating

a) on the production function.

b) above the production function.

c) below the production function.

d) above the isoquant curve.

17. You are an efficiency expert hired by a manufacturing firm that uses K (capital) and L (Labor) as inputs. The firm produces and sells a given output. If w (wage) = $30, r (cost-of-capital) = $20, MPL = 60, and MPK = 60:

a) the firm is cost minimizing.

b) the firm should use less L and more K to cost minimize.

c) the firm should use more L and less K to cost minimize.

d) the firm is profit maximizing but not cost minimizing.

https://brainmass.com/economics/production/cost-minimization-124515

#### Solution Preview

13. Suppose a worker is offered a wage of $10 per hour, plus a fixed payment

of $120 per day, and he can use 24 hours per day. What is the market rate

of substitution between leisure and income?

c) $10.

The market rate of substitution between leisure and income is the variable

wage rate as an individuals needs to forego the variable wage ...

#### Solution Summary

A case of cost minimization is presented.

Profit Maximization, Cost Minimization: Prove that profit maximization implies cost minimization but not vice versa.

Prove that profit maximization implies cost minimization but not vice versa.

I'm looking for a mathematical proof (I think its involving convexity/concavity, I'm not quite sure?)

The types of proofs we learned in class are:

the proofs i learned in class are

Direct Proof. Assume that A is true, deduce various consequences and use them to show that B must also hold.

Contrapositive proof. Assume that B does not hold, then by deducing various consequences show that A cannot hold.

Proof by contradiction. Assume that A is true and B is not true, then show that these assumptions imply a logical contradiction.

I think the answer should satisfy one of the above. I'm not quite sure though.

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