The table shows the total utility TU that Jeremy receives fr

The table shows the total utility (TU) that Jeremy receives from consuming different amounts of two goods, X and Y, per month.

Quantity

TU_X

MU_X

MU_X/P_X

TU_Y

MU_Y

MU_Y/P_Y

0

0

0

1

50

75

2

88

117

3

121

153

4

150

181

5

175

206

6

196

225

7

214

243

8

229

260

9

241

276

Fill in the other columns of the table by calculating the marginal utilities for goods X and Y and the ratios of marginal utilities to price for the two goods. Assume that the price of both goods X and Y is $3. Be sure to use the “midpoint convention” when you fill out the table.

If Jeremy allocates $30 to spend on both goods, how many units will he buy of each?

How much will Jeremy spend on each good at the utility maximizing combination?

How much total utility will Jeremy experience by buying the utility-maximizing combination?

Suppose the price of good Y increases to $6. How many units of X and Y will he buy to maximize his utility now?

Quantity	TUX	MUX	MUX/PX	TUY	MUY	MUY/PY
0	0			0
1	50			75
2	88			117
3	121			153
4	150			181
5	175			206
6	196			225
7	214			243
8	229			260
9	241			276

Solution

MUX MUY 0 0 38 42 33 36 29 28 25 25 21 19 18 18 15 17 12 16 -- -- MUX/PX PUY/PY 0 0 12.66 14 11 12 9.66 9.33 8.33 8.33 7 6.33 6 6 5 5.66 4 5.33 -- --