Problem 3 TwoByTwoByTwo - decentralized (65 points) There are two goods in the economy, food f and leisure l. The economy is populated by 2 consumers, A and B. Their preferences are represented by utility functions, UA (f, l)=2+1 UB (f, l)=+1 Each consumer is endowed with unit of time. Consumption choices are constrained by f 0 and 0. I will now give you an alternative way of understanding how leisure and time works in the slides. Both are valid ways of looking at how time is transformed into consumption goods. Instead of thinking about a market for leisure, think about a labor market where consumers supply labor and firms demand labor. Denote a consumer's supply of labor by h. Denote the price of labor (the wage) by ph. A consumer who supplies h units of labor has labor income phh. Whatever time the consumer does not supply as labor, the consumer takes as leisure. That is, the consumer's time endowment is fully spent on the combination of labor and leisure, 1=l+h. Each consumer has an ownership share of the firm's in the economy which provides dividends, 7, in addition to consumer's labor income. Let p be the price of a unit of food in the economy. With that, the budget constraint of a consumer is, pf Phh+. (1) 1. Demonstrate that the budget constraint in equation (1) can also be written as pf+phl