a quadratic utility function given by 𝑈(𝑥,𝑦)= 𝑥+𝑦−0.05𝑥2−0.05𝑦2 where $90 is the consumer’s budget and the prices of the two goods are, respectively, 4 and 5. What are the optimal values of x and y to maximize the utility function of the cons
a quadratic utility function given by 𝑈(𝑥,𝑦)= 𝑥+𝑦−0.05𝑥2−0.05𝑦2 where $90 is the consumer’s budget and the prices of the two goods are, respectively, 4 and 5. What are the optimal values of x and y to maximize the utility function of the cons
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| Quantity | Tx | Ty |
| 1 | 80 | 100 |
| 2 | 150 | 180 |
| 3 | 210 | 240 |
| 4 | 260 | 280 |
| 5 | 300 | 310 |
| 6 | 330 | 330 |
| 7 | 350 | 340 |
1. If Px= $10, and Py= $20, and consumer's income = $120, find the optimal combination of good X and good Y that will maximize the consumer’s utility.
2. What is the total utility of that combination?
3. If the consumer’s income increases to $150, and prices of goods X and Y are unchanged: a. Find the new optimal quantity of good X and good Y that will maximize the consumer’s utility. b. Calculate the income elasticity of demand for good X, and for good Y, for an income increase from $120 to $150. What can you conclude?
