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The cost of producing q units of a good is C(q) = 50q + 500, and the firm sells q units at p(q) = 500 – 2q. Determine the approximate change in profit when quantity sold changes from 115 to 120. How different is the actual change and the approximate change from each other? 3. %3D

The cost of producing q units of a good is C(q) = 50q + 500, and the firm sells q units at p(q) = 500 – 2q. Determine the approximate change in profit when quantity sold changes from 115 to 120. How different is the actual change and the approximate change from each other? 3. %3D

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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1. Find the linear approximation of F(N) = AK“N®, about N = 1 2. The cost of producing q units of good is C(q) = 0.1q? + 3q + 100 pesos. The firm can sell q units when the price is p(q) = 25 – 0.05q pesos per unit. (Hint: Marginal Cost is C'(q)) Determine the marginal cost, marginal revenue and marginal profit. (Hint: p(q) is not the revenue function). What is the approximate change in cost and revenue when the quantity increases from 20 to 25? a. b. The cost of producing q units of a good is C(q) = 50q + 500, and the firm sells q units at p(q) = 500 – 2q. Determine the approximate change in profit when quantity sold changes from 115 to 120. How different is the actual change and the approximate change from each other? 3. 4. Consider a three-sector economy, Y = C +1+G, where both consumption and investment are a function of income. Consumption is defined as C = a+ bY and I = e + dY Determine the equilibrium level of income. What is the government multiplier? (Hint: getting the derivative of the equilibrium income wrt G) Given that 56% of income is use on consumption, and 12% of income is used on investment. Determine the value for the multiplier effect. If government spending increases by 168, determine the change in equilibrium income. а. b. C.. d. * Determine the total differential of z, 5. x - y z = f(x, y) =: +x*e + In[(2x + y)²] 2xy • Determine the total differential (dg), and total derivative with respect to x g = f(x, y, z) = In(xyz) + e3* + ezy +e* 6. where x = z/3 and y = 5 Find the total differential and total derivative. For the total derivative it is with respect m (or dg/dm) a. g = f(x, y) = 2y3 – xy + 2x2 ,y = 3m x = 6m + 3 7. b. g = f(t, v) = tv, t Inm v = m
Transcribed Image Text:1. Find the linear approximation of F(N) = AK“N®, about N = 1 2. The cost of producing q units of good is C(q) = 0.1q? + 3q + 100 pesos. The firm can sell q units when the price is p(q) = 25 – 0.05q pesos per unit. (Hint: Marginal Cost is C'(q)) Determine the marginal cost, marginal revenue and marginal profit. (Hint: p(q) is not the revenue function). What is the approximate change in cost and revenue when the quantity increases from 20 to 25? a. b. The cost of producing q units of a good is C(q) = 50q + 500, and the firm sells q units at p(q) = 500 – 2q. Determine the approximate change in profit when quantity sold changes from 115 to 120. How different is the actual change and the approximate change from each other? 3. 4. Consider a three-sector economy, Y = C +1+G, where both consumption and investment are a function of income. Consumption is defined as C = a+ bY and I = e + dY Determine the equilibrium level of income. What is the government multiplier? (Hint: getting the derivative of the equilibrium income wrt G) Given that 56% of income is use on consumption, and 12% of income is used on investment. Determine the value for the multiplier effect. If government spending increases by 168, determine the change in equilibrium income. а. b. C.. d. * Determine the total differential of z, 5. x - y z = f(x, y) =: +x*e + In[(2x + y)²] 2xy • Determine the total differential (dg), and total derivative with respect to x g = f(x, y, z) = In(xyz) + e3* + ezy +e* 6. where x = z/3 and y = 5 Find the total differential and total derivative. For the total derivative it is with respect m (or dg/dm) a. g = f(x, y) = 2y3 – xy + 2x2 ,y = 3m x = 6m + 3 7. b. g = f(t, v) = tv, t Inm v = m
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