A firm's total cost and total revenue functions are as follows: 

() = 100 2

()=2352+36+4

(a) Write an expression for the profit function (as a function ofQ) (5%)

(b) Determine the optimal quantity,Q*, that maximizes profits (5%)

Question 2 (5%)

A firm has the following marginal cost function:

()=2226+80

Determine the quantity of output that will minimize its marginal cost.

Question 3 (25%)

The demand curve for haircuts at Terry Bernard's Hair Design is

P= 15-0.15Q

WhereQ is the number of cuts per week andPis the price of a haircut. Terry is considering raising her price above the current price of $9. Terry is unwilling to raise price if the price hike will cause revenues to fall.

2. Should Terry raise the price of haircuts above $9. Why or why not? (15%)
4. Suppose demand for Terry's haircuts increases toP= 22 - 0.22Q. At a price of $9, should Terry raise the price of her haircuts? Why or why not? (10%)

Question 4 (10%)

The Johnson Robot Company's marketing manager estimates that the demand curve for the company's robots in 2008 is:

P = 3000 - 40Q

Where P is the price of a robot and Q is the number sold per month.

2. Derive the marginal revenue curve for the firm. (4%)
4. At whatrange of pricesis the demand for the firm's product price elastic? Justify your answer carefully. (4%)
6. If the firm wants to maximize its total revenue, what price should it charge? (2%)

Question 5 (20%)

The estimated market demand for goodXis:

=70-3.5P-0.6M+4PZ

Whereis the estimated number of units of goodX demanded,Pis the price of the good,Mis income, andPZis the price of the related goodZ. (all parameter estimates are statistically significant at the 1% level.)

2. IsXa normal or an inferior good? Explain. (5%)
4. AreXandZ substitutes or complements? Explain. (5%)
6. AtP=10,M=30, andPZ=6, compute estimates for the price (EP), income (EM) and cross- price elasticities (EXZ). (10%)

Question 6 (15%)

The demand function faced by a firm is the following:

=1008+0.5+2

Where: QX= Quantity demanded of productX

PX= Price of product X

PY= Price of product Y

I = Income

UsingPX= 6,PY= 12,I = 4.5

a) Calculate the point price elasticity of demandEPatPX= 6. (2%)

b) Is demand elastic, inelastic or unitary elastic whenPX= 6? (2%)

c) At this point on the demand for productX, what is the sign of theMR? (2%)

d) How would decreasing the price ofXfrom 6 to 5 affectTR? Explain (2%)

e) Calculate the arc price elasticity of demand betweenPX= 6 andPX= 7. (2%)

f) Calculate the cross-price elasticity for the given values. IsYa substitute or a complementary product toX? (2%)

g) Calculate the income elasticity. IsXa normal or an inferior good? (3%)

Question 7 (15%)

The estimated market demand for goodXis:

=8000-25P-0.12M -30PG

whereis the estimated number of units of goodX demanded,Pis the price of goodX,M is income, andPGis the price of related goodG. (All parameter estimates are statistically significant at the 1 percent level of significance.

a. Is the sign of the coefficient associated with the price consistent with theory? Why or why not? (2%)

b. Given the above equation, is goodXa normal or inferior good? (2%)

c. Are goodsXandGcomplements or substitutes? (2%)

d. AtP = $12,M = $30,000, andPG= $50, what is the predicted quantity of goodX? (2%)

e. At the values in part (d), compute the following elasticities: (3%)

(1) Own Price elasticityEP.

(2) Cross-price elasticityEXG.

(3) Income elasticityEM.

f. All else constant, what would be the effect (in percentage terms) of a 20% increase in income? (2%)

(2%) g. All else constant, what would the effect (in percentage terms) of 15% increase in the price of the related productPG