Compute marginal utilities and marginal rate of substitution for each of the utility functions given below. In each case. explain whether the assumptions of diminishing marginal utility and diminishing marginal rate of substitution are satisfied or not. a) U(X,Y) = 2X-Yy: %3D b) U(X,Y) = XY + 3X + SY c) U(X,Y) = (0.3X +0.7Y") d) U(X,Y) = In (5VX + 2VY) %3D

A consumer has utility (see image) on ice creams (x) and cakes (y).   (a) Are the indifference curves bowed towards the origin? (b) Derive his demand function (as a function of prices px, py and budget I) for ice cream (x).  (c)(Looking at the demand function you found in (b), Is ice cream a normal good? Are ice cream and cakes substitutes or complements? Calculate the income elasticity of market demand at the point px = 2, py = 1 and I = 12.

Only typed solution

3) The utility function of a consumer who consumes quantities x and y of two goods is defined by the expression U(x, y)=√xy subject to the constraint 7x+3y=84 where $84 is the consumer's overall budget. Assuming marginal utilities U,,U>0, maximize the utility function of the consumer. What are the optimal values of x, y and U(x,y) ?

Mia is a registered nurse. She has 18 hours per day to devote to labor or leisure, and has $20 nonlabor income per day. She is paid $10 per hour for the first 8 hours of work and $15 per hour for overtime (for hours worked over 8 hours). Mia's preferences are represented by U(C, R) = CR utility function, where Cis the amount of dollars she spends on consumer goods and R be the number of hours of leisure that she chooses. Question 1 Part a Assuming she can work as many hours per day as she wishes, draw Mia's indif- ference curves, budget constraints and solve for her optimal consumption and leisure choices. Question 1 Part b Suppose that Mia's wage rate rises to $11 an hour for the first 8 hours. She is still paid $15 per hour for overtime. Again, find her optimal choice. Decompose the total change in demand due to a price change into a substitution effect, ordinary income effect and endowment income effect and graphically demonstrate each effect.