Basic Utility Max.) The utility that Sarah receives by consuming fries (F) and c

Question

Basic Utility Max.) The utility that Sarah receives by consuming fries (F) and cake (C) is given by: U (F ,C )= FC . Carefully draw the indifference curves associated with utility level of 24 and utility level of 48. Use a table to show various points on each indifference curve. Use graph paper, make your graph very large, and put cake on the horizontal axis. Are these indifference curves typically shaped (ie: convex)? THINK (use your class handout): What does this tell you about Sarah's preferences for fries and cake? Suppose fries cost $3 a unit, cake costs $2 a unit, and Sarah has $24 to spend on fries and cake. Graph the budget constraint she faces. Calculate the equation of the budget constraint (show work). Your final answer should start with F= Label the utility-maximizing choice of fries and cake point B in your diagram. How many fries and how much cake will she consume to maximize her utility? What are the two criteria that must be met for utility maximization? Carefully explain why these two criteria are met at your answer to part (e). You may need to make a calculation.

Explanation / Answer

Let us take the utility function U= U(x , y). where U stands for utility and x and y are two goods. Now this is a general form of the utility function. You will be given a specific function like U= 4(x+y) + 1/(x+y) What you do is as follows: Take U= 4.25 and find out the different sets values of x and y for which U=4.25. This sets of values give different points on the indifference curve with Utility equal to 4.25. You can see if x= 1 and y= 3, U=4.25. Again, if x= 2, y=2, U=4.25 Again if x= 3, y= 1, U =4.25. Or, x =0, y=4, U=4.25 So, you plot the points (1,3),(2,2), (3,1), (0,4) and (4,0) and join them and you get one indifference curve. To get another indifference curve with higher utility, you can set U=8.50 and find out the values combination of (x,Y) to get the points in the new indifference curve.

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