econ 201 questions

l) (10 pts.) Richard has the following utility function of U = Zln (x1) + x2 where x1 and x2 are the two goods consumed by him. Derive and represent in two separate diagram the demand for x1 and x2 (for any income and prices). 2) (10 pts.) Christina enjoys her expresso with chocolate. She always consumes 4 pieces of chocolate with 2 cups of coffee. Derive and represent in two separate diagram the demand for chocolate and expresso (for any income and prices) 3) (lOpts.) Mark can have milk (M) or soymilk (S) for breakfast. His utility function is: U (M , S) = S + g. Let M represents the number of glasses of milk and S represents the number glasses of soymilk . The price of one glass of milk is $1 and price of a cup of one glass of soymilk is $3. She has an income of $3 to spend for breakfast. Derive and represent in a diagram the demand for milk (for any income and prices) 4) (15 pts) A consumer's utility function is U(x1,x2) = ZSxfxz. The price of x1 is $10 , the price of x2 is $20 and income is y = $300. a) (10 pts.) Price of x] rises from $10 to $40, while price of X2 remains constant. Calculate the new optimal basket. In order to keep her equally satisfy as before, how much income she will need to be compensated for her loss of purchasing power? b) (5 pts.) Is good x1 a normal good? Justify your answer. 5) (20 pts.) John works in a machine factory. Let Y the consumption of other goods (He purchases those goods at a price of $ 1) and let L be the number of hours of leisure that he chooses. John earns $16 an hour and has 18 hours per day to devote to labor or leisure, and he has $32 of non-labor income per day. a) (5 pts.) Write an equation for his budget between consumption of other goods (Y) and leisure (L). Draw his budget line in a graph. b) (10 pts.) If John's utility function over Leisure (L) and other goods (Y) is: U(Y,L) = YL, how many hours of leisure per day will he choose? How many hours per day will he work? 0) (3 pts) Represent the equilibrium graphically. d) (2 pts.) What is John's maximum level of utility 6) (15 pts.) Rich purchases two goods, food and clothing. He has a diminishing marginal rate of substitution of food for clothing. Let x1 denote the amount of food consumed and x2 the amount of clothing. Suppose the price of clothing decrease from 102,1 to 1022- On a Clearly labeled graph, illustrate the income and substitution effects of the price change on the consumption of Clothing. Do so for each of the following cases: a) (7.5 pts.) Clothing is an inferior good, but not a Giffen good. b) (7.5 pts.) Clothing income elasticity of demand is zero