Patrick Mahomes’s utility function is as follows:

U= X+Y^1/2

Where, X, is the quantity of good X consumed, Y, is the quantity of good Y consumed and, U, is Patrick’s utility function.

1. 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?) 

2. 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, P_X, is the unit price of good X, and P_Y, is the unit price of good Y. 

3. What is Patrick’s marginal rate of substitution? Note his respective marginal utilities are MU_X =1 and MU_Y = (½)×Y^-1/2. Please show all of your work to receive full credit.  

4. Derive Patrick’s Marshallian demand equation for good X. Please show all of your work to receive full credit.  

5. 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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Patrick Mahomess utility function is as follows U XY12 Where X is the quantity of good X consumed Y is the quantity of good Y consumed and U is Patric... View the full answer