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(e) Suppose that Duane is faced with the same problem as in (e) except that he has a fixed amount of K. In fact, K = 16. How much F should be bought to minimise costs? What is the total cost?

(e) Suppose that Duane is faced with the same problem as in (e) except that he has a fixed amount of K. In fact, K = 16. How much F should be bought to minimise costs? What is the total cost?

Principles of Microeconomics
Principles of Microeconomics
7th Edition
ISBN:9781305156050
Author:N. Gregory Mankiw
Publisher:N. Gregory Mankiw
Chapter7: Consumers, Producers, And The Efficiency Of Markets
Section: Chapter Questions
Problem 6CQQ
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Please answer question 3-e it's on page 2 as i uploaded 2 files

1. The American Mining Company is interested in obtaining quick estimates of the supply and demand curves for coal. The firm's research department informs you that the elasticity of supply is approxi- mately 1.7, the elasticity of demand is approximately -0.85, and the current price and quantity are $41 and $1,206, respectively. Price is measured in dollars per ton, quantity is captured as number of tons per week. (a) Is demand elastic, inelastic or unit elastic? Explain. (b) Write down the linear supply and demand curves at the current price and quantity. (c) Using Excel, provide a graph of the demand and supply curves. Is the market in equilibrium? (d) Calculate the Total Revenue, Average Revenue, and Marginal Revenue of the American Mining Company at the equilibrium price and quantity. 2. Sally consumes two goods, X and Y. Her utility function is given by the expression U = 3XY2. The current market price for X is £10, while the market price for Y is £5. Sally's current income is £500. (a) Sketch a set of two indifference curves for Sally in her consumption of X and Y. (b) Write the expression for Sally's budget constraint. Graph the budget constraint and determine its slope. (c) Determine the X,Y combination which maximises Sally's utility, given her budget constraint. (d) Calculate the impact on Sally's optimum market basket of an increase in the price of X to $15. What will happen to her utility as a result of the price increase? 3. Duane breeds parrots for a living. He has discovered that the production function for parrot chicks is: Q=K0.5 F0.5 where K is capital (for example nest boxes, cages and the like) and F is parrot food. The price of K is $8 and the price of F is $2. (a) What type of production function is this? Explain. (b) Does this production function exhibit constant, increasing or decreasing returns to scale? Provide a graph of the function using Excel. (c) Find the marginal products of capital and food. (d) Suppose that Duane wants 144 parrot chicks, how much K and F should be employed to minimise costs. What is the cost of producing 144 parrot chicks? 1
Transcribed Image Text:1. The American Mining Company is interested in obtaining quick estimates of the supply and demand curves for coal. The firm's research department informs you that the elasticity of supply is approxi- mately 1.7, the elasticity of demand is approximately -0.85, and the current price and quantity are $41 and $1,206, respectively. Price is measured in dollars per ton, quantity is captured as number of tons per week. (a) Is demand elastic, inelastic or unit elastic? Explain. (b) Write down the linear supply and demand curves at the current price and quantity. (c) Using Excel, provide a graph of the demand and supply curves. Is the market in equilibrium? (d) Calculate the Total Revenue, Average Revenue, and Marginal Revenue of the American Mining Company at the equilibrium price and quantity. 2. Sally consumes two goods, X and Y. Her utility function is given by the expression U = 3XY2. The current market price for X is £10, while the market price for Y is £5. Sally's current income is £500. (a) Sketch a set of two indifference curves for Sally in her consumption of X and Y. (b) Write the expression for Sally's budget constraint. Graph the budget constraint and determine its slope. (c) Determine the X,Y combination which maximises Sally's utility, given her budget constraint. (d) Calculate the impact on Sally's optimum market basket of an increase in the price of X to $15. What will happen to her utility as a result of the price increase? 3. Duane breeds parrots for a living. He has discovered that the production function for parrot chicks is: Q=K0.5 F0.5 where K is capital (for example nest boxes, cages and the like) and F is parrot food. The price of K is $8 and the price of F is $2. (a) What type of production function is this? Explain. (b) Does this production function exhibit constant, increasing or decreasing returns to scale? Provide a graph of the function using Excel. (c) Find the marginal products of capital and food. (d) Suppose that Duane wants 144 parrot chicks, how much K and F should be employed to minimise costs. What is the cost of producing 144 parrot chicks? 1
(e) Suppose that Duane is faced with the same problem as in (e) except that he has a fixed amount of K. In fact, K = 16. How much F should be bought to minimise costs? What is the total cost? 4. Consider the following Keynesian national-income model, Y=C+ Io + Go C = a + b(Y - To) where a and b are parameters with the following range; a>0 and 0<b<1. Y represents national income, C is consumption expenditure, Io is investment, Go is government spending, and To taxation. (a) What are exogenously determined variables in this model. (b) Show that this model can be expressed in the following matrix form: (7) (x) = (1 + Go) (c) Using matrix algebra, find the solution for Y and C. (d) Suppose government spending increases by some amount AGo to become Go+AGo. Show the change in Y and C as a response to this increase in spending.
Transcribed Image Text:(e) Suppose that Duane is faced with the same problem as in (e) except that he has a fixed amount of K. In fact, K = 16. How much F should be bought to minimise costs? What is the total cost? 4. Consider the following Keynesian national-income model, Y=C+ Io + Go C = a + b(Y - To) where a and b are parameters with the following range; a>0 and 0<b<1. Y represents national income, C is consumption expenditure, Io is investment, Go is government spending, and To taxation. (a) What are exogenously determined variables in this model. (b) Show that this model can be expressed in the following matrix form: (7) (x) = (1 + Go) (c) Using matrix algebra, find the solution for Y and C. (d) Suppose government spending increases by some amount AGo to become Go+AGo. Show the change in Y and C as a response to this increase in spending.
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