the level of production. In particular, the demand equation for the product is P

Question

the level of production. In particular, the demand equation for the product is P(a) C(a) 4q+7. Suppose that 0 s9S 700. pany has estimated that the price it can charge for its product fuctuates with 3 +3000. (P(a) is in dollars.) The cost of production in dollars is given by (a) Express the company's revenue as a function of q. That is, write down the revenue function, R(g) (b) Express the company's profit as a function of q. That is, write down the profit function, ? (g). T(a) (c) Compute the marginal cost at q 100 units. MC(100) (d) Compute the marginal revenue at q 100 units. MR(100)_ (e) Should the company increase or decrease production from 100 units in order to gain more profits? Explain why in terms of marginal cost and marginal revenue.

Explanation / Answer

3) a) The revenue is the product of the demand and unit of production. So,

R(q)=(-3q+3000)q= -3q^2+3000q

b) Profit=revenue-cost

So, Pi(q)=R(q)-C(q)=(-3q^2+3000q)-(4q+7)= -3q^2+2996q-7

c) Marginal cost, C'(q)=4, at q=100, the marginal cost is C'(100)= 4

d) Marginal revenue, R'(q)=-6q+3000

so, at q=100, the marginal revenue is R'(100)= -6(100)+3000= 2400

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