Patrick Mahomess utility function is as follows: U = X+Y 1/2 Where, X , is the quantity
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Patrick Mahomes’s utility function is as follows:
U= X+Y1/2
Where, X, is the quantity of good X consumed, Y, is the quantity of good Y consumed and, U, is Patrick’s utility function.
- Suppose Patrick’s utility is 5. Use EXCEL to draw his indifference curve when good ‘Y’ varies from 1 to 25 by increments of 1. Use the scatter plot in EXCEL to graph this indifference curve. Is this curve indicative of substitute goods? (i.e., is the indifference curve convex to the origin?)
- If Patrick spends all of his income, B, on goods X and Y what is the general form of his budget constraint? (Hint: the budget constraint should be specified such that budget is the sum of the expenditures on good X and Y.) Also note that you should use notation such that, PX, is the unit price of good X, and PY, is the unit price of good Y.
- What is Patrick’s marginal rate of substitution? Note his respective marginal utilities are MUX =1 and MUY = (½)×Y-1/2. Please show all of your work to receive full credit.
- Derive Patrick’s Marshallian demand equation for good X. Please show all of your work to receive full credit.
- Suppose now that Patrick’s income is $1000 and the price of good Y is 1. Accurately graph Patrick’s Marshallian demand curve for good X for prices ranging from 1 to 25 by increments of 1. You must graph the demand curve for good X to receive credit. Please show all of your work to receive full credit. You are encouraged to use EXCEL to complete this question.
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