Question1A consumer has autility function𝑈=𝑋!𝑋”Where𝑋!and𝑋”are the consumed quantities ofA andB,and an initial endowment/allocation of𝑋!$$$$=2and𝑋”$$$=1. The prices of these goods are given and equal to

1.a)Set up the consumer budget constraint.

b)Plot it/Represent it graphically.c)Calculate the optimal basket.

Question2Consider an economy with two periodswhere individuals have perfect access to credit, which has an interest rate of 0.20.The utility function of consumers is given by:𝑈(𝑐#,𝑐$)=𝑙𝑛𝑐#+𝛽𝑙𝑛𝑐$In each period the consumer has a variable nominal income,which depends on his experience in the job market. In the first period,the income is 100,and in the second period the income is 150.The consumption prices in each period are respectively p1 = 1 and p2 = 2.Consideringthis, calculate and answer:a.The amount consumed in each period.b.Is the consumer a saver of loans or a borrower?c.Suppose that the consumption price in period 2 increases to 2.5.c.1What will happen to consumer choices?c.2.Interpret economically what happens to his choices.d.Suppose the interest rate drops to 0.10.d.1What will happen to consumer choices?d.2Interpret economically.e.Answer:e.1What happens if β = 0?e.2Interpret economically.Question3Maryis a teacher who has 10 hours a day to allocate between work and leisure. For each hour worked, Mary receives $10. Her basket price is $2. Mary’s utility function is given by:𝑈(𝐶,𝑅)=𝐶%𝑅$

a)Calculate the number of hours that Marywill dedicate to leisure and work per day. Show the leisure demand function and the consumption demand function.b)Suppose the hourly wage rises to $20.b.1)What will happen to the demand for consumption and the demand for leisure?b.2)Will Mary reduce or increase the number of hours worked? Why?c)Suppose now that in addition to the income she earns from work, Mary has a property that is rented for $10. With the income from work, will Mary change her budget constraint? Why