A consumer has a utility function of his two consumption activities, child care (X) and food (Y). The utility function is represented by U = X^(0,2)Y^(0,8). The price of Y is Px = 2 , the price of X is Py = 4 and the consumer's income is I = 20.

1. Show the demand function for child care (X) and consumer food (Y). What is the best number of child care and meal units for this consumer? How much utility does the consumer enjoy?
2. Suppose the government provides subsidies in the form of money, S = 10 units of money to these consumers. Show how the consumer allocates the subsidies received on his consumption? What is the optimal amount of child care (X) and meals (Y) after receiving the subsidy? How much utility does the new consumer enjoy? Graph the consumer's equilibrium condition before and after receiving subsidies on a graph (horizontal axis for child care, X, and vertical axis for food, Y)
3. Suppose the government changes its subsidy policy. The government provides subsidies in the form of goods, namely 4 hours of child care (X) and 0.5 units of food (Y). Assume that subsidized goods cannot be traded. Draw the condition of the budget line before and after the provision of subsidies (horizontal axis for child care, X, and vertical axis for food, Y). Also show the balance of consumers before and after receiving subsidies. What is the best child care and food consumption for the new consumer? How much utility do consumers perceive?
4. From your answers b) and c), which do you think is better for consumers? Explain your reasons.