Question

Q1- A manufacturer estimates that its variable cost for manufacturing a product is given by the following expression: C(q) = 25q 2 + 2000q [$] where C is the total cost and q is the quantity produced. Derive expressions for the revenue and the profit, substitute if q=10

Q2- Economists estimate that the supply function and demand function for the widget market is given by the following expressions: q = 0.2 · π − 40 π = −10q + 2000 π = 5q + 200 Draw demand and supply curves as a function of q and calculate; a- the demand and price at the market equilibrium.
b- For this equilibrium, calculate the consumers’ gross surplus, the consumers’ net surplus, the producers’ revenue, the producers’ profit and the global welfare.

Answer 1

You have asked multiple unrelated questions in the same post. I have addressed the first question. Please post the balance question, separately.

Also please don't downvote the solution merely because I have answered only one question. Please!!

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Q - 1

C(q) = 25q² + 2,000q

The company will produce and sell till the time revenue per unit= marginal cost

Marginal cost = dC(q)/dq = 50q + 2,000

Hence, revenue per unit = marginal cost = 50q + 2,000

Hence, expression for revenue = R(q) = Reveue per unit x q = (50q + 2,000) x q = 50q² + 2,000q

And expresssion for profit = P(q) = R(q) - C(q) = 50q² + 2,000q - (25q² + 2,000q) = 25q²