Fred consumes goods x and y. His utility function is U(x, y) = x² y .

He is endowed with 30 units of x and 12 units of y.

The price of x is $4 and the price of y is $8.

a. Fred will buy fewer than 5 units of x

b. Fred will sell fewer than 5 units of x

c. Fred will buy fewer than 5 units of y

d. Fred will buy 5 or more units of y

e. Fred will buy at least 5 units of x

FOR THIS QUESTION, HOW DO I KNOW WHEN HE BUYS OR SELLS UNITS? I know how to determine the quantities but I am not sure how to determine buying and selling.

Nathan earns 15 dollars an hour. He has nonlabour income of $180 per week.

He has 80 hours a week available for either labour or leisure.

His utility function is U(c, r) = c² r, where c is dollars' worth of goods and r is hours of leisure.

How many hours per week will he work.

a. At least 64 hours per week (64 or more)

b. At least 48 hours per week but fewer than 56 hours per week

c. At least 40 hours per week but fewer than 48 hours per week

d. At least 56 hours per week but fewer than 64 hours per week

e. Fewer than 40 hours per week

Rose has an income of $800 in period 1 and will have an income of $1200 in period 2.

Her utility function is U(C₁, C₂) = C₁^0.8 C₂^0.2, where c₁ is consumption in period 1 and c₂ is consumption in period 2.

The interest rate is 0.5 (50%).

If she unexpectedly won a lottery at the start of period 1, which pays its $3000 prize at tge start of period 2, (so that her income in period 2 would be $4,200 and her income in period 1 remains $800), then her consumption in period 1 would

a) increase to double her "no-prize" consumption in period 1

b) increase to an amount more than double her "no-prize" consumptio in period 1

c) increase by less than $1200

d) not change as the pize will not be received until period 2

e) increase by at least $1200 but by less than double her "no-prize" consumption in period 1

Steve and Joe consume two goods, x and y. They have identical Cobb-Douglas utility functions: U(x,y) = x³y²

Initially Steve owns 30 units of x and 30 units of y. Initially Joe owns 50 units of x and 90 units of y.

They make exchanges to reach a Pareto optimal allocation.

Which of the following is not necessarily true about the allocation to which they trade?

a) Steve consumes 3 units of y for every 2 units of x that he consumes.

b) The locus of Pareto optimal allocations is a diagonal straight line in the Edgeworth box.

c) Joe consumes more units of y than he consumes units of x.

d) Joe consumes more than 50 units of y.

e) Steve consumes fewer than 30 units of x.

Consider a single-input production technology, Q(L) = L^(1/2) = sqrt(L), where Q is output and L is the amount of labour input used.

The competitive market price of output is $120, and the wage rate is $15 per labour unit (person-hour).

At the profit-maximizing quantity of labour employed,

a) The firm`s profit equals the firm`s total cost of labour

b) The consumer/labour - supplier is maximizing utility

c) The real wage is equal to the price of output

d) The slope of the production function = 8

e) The price of output is equal to the marginal product of labour.

Trying this again because last time answers provided were wrong. Please show full calculations and explanations, thank you.