Suppose honey is produced in a beehive using bees and sugar. Each honey producer
ID: 1185703 • Letter: S
Question
Suppose honey is produced in a beehive using bees and sugar. Each honey producer uses one beehive which she rents for $20/month. Producing q gallons of honey in one month requires spending 5q dollars on bees, and 4q^2 on sugar. 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=512-4P. Also, suppose there are 50 honey producers in the market. What is the equilibrium price of honey? How much profit does an individual producer make in a month?
Explanation / Answer
Fixed costs:
FC =$20/month
Variables costs
VC = 5q + 2q^2
Total costs
TC = 20 + 5q + 4q^2
The marginal cost is the derivative of this with respect to q.
MC = 5 + 8q
And the short run supply curve is the marginal cost that lies above the average variables cost.
Average variable cost is:
AVC = VC/q
AVC = (5q + 4q^2)/q
AVC = 5 + 4q
So, the supply curve is:
SRS = 5 + 4q if P> 5 + 8q
Thus:
equilibrium price=P=5+8*Q/50
50P=250+8*(512-4P)
P= $53
profit does an individual producer make in a month :
Q =512-4*53 = 300
q = 300/50 =6
TC = 20+5*6+4*6^2 = 194
Market price = 53*6 = 318
Profit = 318-194 =$124