Question

Q1- A manufacturer estimates that its variable cost for manufacturing a product is given by the...

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.

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

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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

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