Question

(20 points) Suppose honey is produced in a beehive using bees and sugar.  Each honey producer uses one beehive which she rents for $40/month. Producing q gallons of honey in one month requires spending 4q dollars bees, and 2q²dollars on sugar.

a) (4 points) What is the total cost of producing q units of honey for an individual honey producer in a given month?

b) (4 points) In general, if the total cost of producing honey is a + bq + cq², then the marginal cost of producing honey is b + 2cq.  Assuming each honey producer operates as a price-taker, what is the monthly supply curve for an individual producer?

c) (4 points) Let Q be the total market supply, and q is the supply of an individual firm.  Therefore, q = Q/n where n is the total number of firms in the market.   Suppose the demand for honey is given by Q = 548-4P.  Also, suppose there are 60 honey producers in the market.  What is the equilibrium price of honey?

d) (4 points) How much profit does an individual producer make in a month?  

e) How many firms will there be in long run equilibrium?  (Remember, a firm will enter the market as long as it can make a positive profit, otherwise a firm will not enter the market.)

Answer 1

a) What is the total cost of producing q units of honey for an individual honey producer in a given month?

Total Cost, TC=Rental Cost+ Bees Cost+ Sugar Cost

TC=40+4q+2q²

b) In general, if the total cost of producing honey is a + bq + cq², then the marginal cost of producing honey is b + 2cq.  Assuming each honey producer operates as a price-taker, what is the monthly supply curve for an individual producer?

Marginal Cost=MC=dTC/dq=d(40+4q+2q²)/dq=4+4q

We can also use the information given in the question and directly get the Marginal Cost

Step 1 , Compare the given format with TC function and get the values of constants

b=4

c=2

So, Marginal Cost, MC=b+2cq=4+2*2q=4+4q

Since every honey producer is a price taker. It sets its output level q such that

Price, P=MC

So, P=4+4q

It gives the supply curve of individual producer.

Sometimes supply curve is also given as q in terms of p

P=4+4q

on rearranging we get

4q=-4+P

q=-1+0.25P

Supply curve of individual producer will be given by

q=-1+0.25P

c) Let Q be the total market supply, and q is the supply of an individual firm.  Therefore, q = Q/n where n is the total number of firms in the market.   Suppose the demand for honey is given by Q = 548-4P.  Also, suppose there are 60 honey producers in the market.  What is the equilibrium price of honey?

Market Supply Curve for honey=No. of honey producers*supply =60*q=60*(-1+0.25P)=-60+15P

In equilibrium, Market Demand=Market Supply

548-4P=-60+15P

15P+4P=548+60

19P=608

P=32 per unit

d) How much profit does an individual producer make in a month?

We have derived individual supply curve in part(b)

q=-1+0.25P

Put P=32

q=-1+0.25*32=7

Total Cost, TC=40+4q+2q²

TC=40+4*7+2*7^2=166

Total Revenue=TR=P*q=32*7=224

Profit=TR-TC=224-166=58

It individual producer makes a profit of 58 per month in the short run.

e) How many firms will there be in long run equilibrium?  (Remember, a firm will enter the market as long as it can make a positive profit, otherwise a firm will not enter the market.)

Producers are making positive profit in this case. So, other firms will start entering the market. It will lead to increase in market supply. Naturally prices will start decreasing in this scenario. Individual profits will also start decreasing. In long run economic profit of each producer will be zero

We have derived the following relations earlier

TC=40+4q+2q²

MC=4+4q

Average total cost, ATC is given by

ATC=TC/q=(40+4q+2 q²)/q=4+2q+(40/q)

In long run

ATC=MC

4+2q+(40/q)=4+4q

2q=40/q

2q²=40

q= 4.472136

P=4+4q=4+4* 4.472136=21.88854

Market demand at P=21.88854, is

Q=548-4P=548-4*21.88854=460.4458

Number of producers/firms=N=Q/q=460.4458/4.472136=102.9588 or say 103