1. If the price of good X is $1.00, the price of good Y is $2.00, and the consumer's income is $36.00, find the optimal consumption bundle for a consumer who is always willing to trade 4 units of Y for 1 unit of X.
2. Vasco's utility function is U=10X2Z, the marginal utility of X is MUX=20XZ, and MUZ = 10X2. The price of X is $10, the price of Z is $5 and his income is Y=$150. What is his optimal consumption bundle? And show this bundle on graph.
3. Placing the good X on the horizontal axis and good Y on the vertical axis, graphically illustrate the income and substitution effects of an increase in the price of good X. Please assume that both goods are normal goods.
4. Professors Kubik and Black make up the entire demand side of the market for summer research assistants in the economics department. If Kubik's demand curve is QK = 25 - (1/2)P and Black's is QB = 100 - P. What is the market demand curve for research hours in the economics department?