**Full solutions for assignments**

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**1. **Suppose that consumer is spending all of his income on goods A and B. The price per unit of good

A is 20 Euros and the price per unit of good B is 10 Euros. Consumer’s income is 400 Euros.

**a) **Describe the consumption possibilities of this consumer by the budget line equation. *(Please state clearly, which variable in your equation denotes the quantity if good A and which variable denotes the quantity of good B. Similarly define clearly, which variable denotes the price of good A and which variable denotes the price of good B).*

**b) **Describe the consumption possibilities of this consumer graphically: draw the budget line, identify the numerical values of intercepts and the slope of the budget line *(Don't forget to label the x- and y-*

*axis**)*

**c) **What is the opportunity cost of consuming 4 units of good A for this consumer?

**d) **Suppose that Government is planning to apply an income tax of 20% with regard to consumer’s income and, at the same time, is going to apply also a tax of 20 Euros per unit of good A. Describe the consumer’s consumption possibilities after these Government policies: write the new budget line equation *(NB! There is no need to draw the budget line for this scenario.)*

* *

**2. **Describe mathematically (by the utility function) and graphically (by the indifference curves) the preferences of the consumer who consumes good A and good B always together (and never

separately), in ratio four units of good B per one unit of good A. *(Please denote the quantity of good A by letter A and the quantity of good B by letter B. Don't forget to label the horizontal and vertical axis and identify the numerical values of intercepts).*

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**3. **The consumer’s utility function is U(a,b) = a + 4b, where *a *denotes the quantity of good A that the consumer consumes and *b *denotes the quantity of good B that the consumer consumes. The price per unit of good A is 6 Euros and the price per unit of good B is 12 Euros. Consumer’s income is 2400 Euros. Find the optimal quantity of good A and good B consumed by this consumer.

**4. **The consumer’s utility function is U(x,y) = xy2, where x denotes the quantity of good X that the consumer consumes and y denotes the quantity of good Y that the consumer consumes. Thus, for the consumer, the marginal utility of good X is MUx = y2 and the marginal utility of good Y is MUy = 2xy. The price per unit of good X is 12 Euros and the price per unit of good Y is 4 Euros. Consumer’s income is 3600 Euros. Find the optimal quantity of good X and good Y consumed by this consumer.

**5. **Consumer’s income is 720 Euros, the price per unit of good X is 6 Euros, the price per unit of good Y is 12 Euros, consumer’s utility function is U(x; y) = min {x; 4y} *(y denotes the quantity of good Y and x denotes the quantity of good X that the consumer consumers)*. *consumer consumers)*.

**a) **Find the optimal quantity of good X and good Y, for this consumer **b) **Government is considering 2 alternative taxation schemes: - alternative 1:a tax of 4 Euros per unit of good Y - alternative 2:an income tax of 25% on consumers’ income

If the consumer has to choose one of the taxation schemes, then which of these taxation schemes will the consumer choose? Provide calculations for proof**.**

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**6. **The consumer’s demand for good X is determined by the function X* (Px, M) = M / 5Px , where Px denotes the price per unit of good X. Consumer’s income is 3000 Euros, the price per unit of good X is20 Euros and the price per unit of good Y is 10 Euros. Suppose that the price per unit of good X increases by 10 Euros *(thus, the new price per unit of good X is 30 Euros)*. Given this price increase of X:

**a) **calculate the total change in the consumer’s demand for X? **b) **calculate the substitution effect according to Slutsky? **c) **calculate the income effect according to Slutsky?

**7. **Market demand for good Y is described by function YD = 80-PD, where PD is the demand price and YD is the quantity of good y demanded. Market supply of good Y is given by function YS = 20+PS, where PS is the supply price and YS is the quantity of good y supplied.

**a) **Find the market equilibrium quantity and equilibrium price.

**b) **Suppose that a tax 20 euros is applied per unit of good Y, while the rest of the factors that could affect demand or supply remain unchanged. Find the market equilibrium (the equilibrium quantity, the demand price and the supply price) that will exist in this market after this tax.

**c) **Suppose that a subsidy 10 euros is applied per unit of good Y, while the rest of the factors that could affect demand or supply remain unchanged. Find the market equilibrium (the equilibrium quantity, the demand price and the supply price) that will exist in this market after this subsidy.

Subject | Business |

Due By (Pacific Time) | 10/20/2014 02:00 pm |

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