Question

1.Calculate the midpoint price elasticity of demand using the price of $5 and $7. The demand function is:
Q = 1,500 - 200P
Where Q is quantity demanded and P is price.


2.A new company estimates fixed costs for its product of $50,000 per year and average variable costs of:
AVC=$0.5+$0.0025Q,
Where AVC is average variable cost (in dollars) and Q is output.
Calculate total cost and average total cost for the projected first-year volume of 20,000 units.


3.Calculate profit from the following demand and total cost functions at output level of 160 units:
Q = 448 - 16P
TC = 1000 + 5 Q

Answer 1

$$p_1=5, Q_1=500$$

$$p_2=7, Q_2=100$$

$$E=\frac{Q_2-Q_1}{p_2-p_1}\times \frac{p_1+p_2}{Q_1+Q_2}=-4$$

2

$$TC=FC+VC$$

$$VC=AVC \times Q=0.5Q+0.0025Q^2$$

$$TC=50000+0.5\times20000+0.0025\times 20000^2=1060000$$

$$ATC=\frac{TC}{Q}=53$$

3

$$p=\frac{448-Q}{16}$$

$$TR=pQ=\frac{448Q-Q^2}{16}$$

$$Pr=TR-TC$$

$$Pr=28Q-\frac{1}{16}Q^2-1000-5Q$$

$$Pr=23 \times160-1600-1000=2080$$