# John Hopkins Ss Intermediate Microeconomics Problem Report – assignmentcollections.com

Business Finance Assignment Collections – assignmentcollections.com

Problem Set 1

Due electronically by the due date to be announced in class and/or through Blackboard

Instructions: Answer all parts of the following four problems. To receive full credit all work must be shown. Illegible or sloppy work will receive a grade of zero. Late problem sets will not be accepted. Be sure to carefully follow any additional instructions given below.

# 1Supply-Demand analysis

Let the inverse market demand and supply curves for an arbitrary good be given by

and

( ) = −

( )= + ,

respectively, where (conversely, ) denotes quantity demanded (conversely, quantity supplied) and all lower-case Greek letters denote positive parameters such that > > 0 and

>

(a)Solve for the market equilibrium price ( ) and quantity ( ) and show this solution on a supply-demand graph.

= 2, = 3. Determine the corresponding equilibrium values for the market price, quantity transacted, and own-price elasticity of market demand. Repeat this exercise now assuming that = 20 and all other estimated model parameters remain the same.How do your results comport with the comparative statics predictions derived in parts (b) and (d)?

# 2Marginal rates of substitution

Find the marginal rate of substitution ( , ) for each of the following utility functions: (a) ( , ) = 3 +

(b) ( , ) = 2 2

(c) ( , ) =

+

(d) ( , ) = min{ , 2 }

(e) ( , ) =ln + ln

# 3Utility and consumption choices

Sam Spade is a detective. He consumes only two goods: rot gut whiskey ( ) and unfiltered cigarettes ( ). Suppose that his utility function is given by:

1

( , ) = 2( + 1)3

vs. 2 bottles of whiskey and 6 packs of cigarettes.

( , ) =

6( + 1)4

.

7

1 1

( , , ) = 2( + 1)3 2 .

Calculate Sam’s new , and discuss the impact of poetry on this expression relative to the result found in part (a).

# 4Comparative statics and demand [harder]

For each of the following two-good utility functions:

• ( , ) = − (1 − 0.5 2
• ( ,

1221 )

) = 1−1

for

> 1, 0 < < 2

12( 2−2)212

(do not concern yourself with second-order conditions when solving this problem)

• Write down the consumers’ utility maximization problem and the associated Lagrangian function;
• Derive the first-order (necessary) conditions (FOCs) with respect to 1, 2, and
• Compute and sign the comparative statics terms , , and
• Compute the own-, cross-, and income-elasticities of demand corresponding to the demand functions calculated in part (iii) (i.e., , , ).

(assume throughout that all endogenous variables are strictly positive);

 1

Use the FOCs from part (ii) to solve explicitly for the consumer’s demand functions,

 2

and
, as expressed in terms of all relevant model parameters;

∗ ∗

∀ , = {1,2} , ≠ .

Provide an economic interpretation of your results and note any “unusual” characteristics of these demand functions.

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