EC2A1: Microeconomics II Class 1: Exercise and Solution

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EC2A1:  Microeconomics II

Class 1:  Exercise and Solution

There are two groups of individuals in a country: “fish & chip”1 producers F, and co↵ee-shop baristas,  B . There are 80“fish & chip”producers and 10 co↵ee-shop baristas. All individuals like to eat fish & chips, x1  and drink co↵ee x2 . They have identical preferences:

x 1(J) +2qx2(J)

where J 2 {F,B}. The prices of fish & chips and co↵ee are p1  and p2 . Each fish & chip producer makes 1 portion of fish and chips and each co↵ee barista makes 1 cup of co↵ee.  You can assume that non-satiation and convexity hold, and you can focus on interior solutions. They sell their produce in a competitive market.

1. Derive the demand functions for fish & chips and co↵ee when prices are fixed.

2. What is the equilibrium price ratio between fish & chips and co↵ee (hint, set p1  = 1 and solve for p2 ).

3. What are the utilities of each F and B individuals at this price ratio?

4. Now suppose that the country opens up to migration which results in

10 new fish & chip producers and 20 new co↵ee-shop baristas moving to the country (nobody leaves). The migrants have the same preferences and are as productive as the existing producers, each making one unit of output of their respective good. What is the new equilibrium price ratio between fish & chips and co↵ee? Explain your finding intuitively.

5. How does the utility of type F and B individuals change after migration compared to before? Explain you answer intuitively.

6. Why is it important to think about the impact of migration in general equilibrium terms?

7. Does the framework help to think about gainers and losers as a conse- quence of labour migration? Is the mechanism in the model realistic? What does it leave out?

1    Solution

1. Set p1   = 1. Then substitute the budget constraint into the utility

function to

Then

so

get:

x 1(J)

mJ  − p2 x2(J) +2qx2(J)

p2  =

x2(J)  =

 

= mJ  − p2      1       = mJ  −  1


mF     =  1 and mB  = p2 

2. Set aggregate supply equal to aggregate demand for good 2:  = 10

then

p2  = 3.

3. To derive the utilities substitute the prices into the demands and plug them into the utility functions. The utilities are:

F   : 1 − p2 x2(F) +2qx2(F)  = 1 −  +2 ⇥  =  B   : 3 − p2 x2(B)  +2qx2(B)  =  .

4. The individual demands for the goods have not changed. We just need to clear the market again:

 = 30

so

p2  = 2.

We have increased supply relative to demand so the price of co↵ee has fallen relative to fish & chips.

5. Utilities are now:

F   : 1 − p2 x2(F) +2qx2(F)  = 1 −  +2 ⇥  =  >  B   : 2 − p2 x2(B)  +2qx2(B)  = 2 +  =  <  .

So F has gained because the price of co↵ee has fallen and B has a lower utility because she is a producer of co↵ee and benefits as a consumer are lower than costs as a producer.

6. Price changes determine the pattern of gainers and losers. This matters to people who produce goods as well as those who con- sume. You would not see this at all without a general equilibrium approach.

7. For class discussion; take notes when you attend class.  There are no right or wrong answers here, but in an exam question like this, it is important to be reflective and intelligent, showing that you understand the role of a model.  Here, that would mean noting that by changing relative prices, migration a↵ects the whole economy and of course this is a↵ected by the skill composition of migrants. But migration is a much more complex issue than this, with political and social dimensions not just economics.  And to trace through the full general e↵ects across an economy with many sectors and goods would require a lot of data. The impact of migration on wages and incomes is quite hard to pin down when migrants flow to particular destinations endogenously. `u


2023-02-25