Skip to main content

Exercise: pegged exchange rate

  • Assume that the U.S government wants to start fixing its currency against the Mexican peso. Government officials estimate that the optimal exchange rate should be at one peso for $0.35.
  •  You are given the following information about the U.S market for Mexican peso:
  • Find how much peso does the U.S needs to buy or sell in order to achieve its targeted exchange rate.
    • Find the original equilibrium exchange rate: let the demand equal to the supply curve. Just like in the previous exercise, we see that one peso is worth half a U.S dollar and there are 6,250,000 pesos demanded at this price.
    • Now, in order to change the exchange rate, realize that the U.S government has access to U.S dollars (for the sake of the argument, assume the central bank is no longer independent). Then, it can only shift the demand for Mexican pesos in the U.S foreign exchange market.
    • Thus, there must only be a movement along the supply curve, set $=0.35 in the supply schedule and solve for p.
    • Now, calculate the gap between the new equilibrium exchange rate and the exchange rate given in the old demand:
    • Substract that gap from the original demand and obtain the new demand curve. Set the new demand curve equal to the supply curve and solve the system. We see that in order to obtain this new exchange rate, the U.S government needs to sell 1,500,000 worth of Mexican financial assets in order to buy back U.S dollars. This is the difference between the old and new equilibrium amount of Mexican pesos.
    • Note that since the Mexican peso is depreciating, it must be the case that the U.S dollar is appreciating. 
  • Let's graph that:

Comments

Popular posts from this blog

Macroeconomics: multiplier and crowding out effects

Multiplier effect: whenever   any of the components of AD increases, the increase in GDP will be greater than the initial increase in expenditures. The impact on GDP of a particular increase in spending depends on the proportion of the new income that is taken out of the system to the proportion that continues to circulate in the economy. The multiplier effect tells us the impact a particular change in one the components of AD will have on the total income (GDP).  Let k denote the spending multiplier, which is a function of MPC and MPS. The larger the marginal propensity to consume, the larger the spending multiplier. Notice that the larger the MPC, the greater the impact a particular change in the spending variables will have on the nation's GDP. The crowding out effect: If government spending increases without an increase in taxes, the government must borrow funds from the private sector to finance its deficit, thereby increasing the interest rate. This increase in interest ...

Exercise: maximizing profit

Assume that you are the owner of a small business that produces T-shirts. Your the total revenue for your business can be modeled by the following equation: and your total cost corresponds to this function: Find the point at which your firm maximizes its profit. Then, find how much profit the firm if able to earn at that point. Using the total cost and total revenue functions we can set up the profit function: Then, realize that if you want to find the maximum profit, take the derivative of the function and set it up equal to zero, and solve for Q. This is equivalent of taking the derivative of the total cost and total revenue functions and setting them equal to each other. In this problem, I chose the latter option as it was explained in the previous lessons. Notice that profit is often denoted by a capital pi.  We are assuming that the TR>TC for some positive value, you can check for yourself. However, if we did not know that, we would first take the first ...

A short interlude...

Hello all, it's been quite some time since I have made any major announcements since the creation of this blog about a year and a half ago. I am currently in graduate school and will soon take a portion of my comprehensive examination (i.e exams in Micro, Macro, and Metrics that will allow me to continue my studies in my graduate program), wish me luck! Thus, I will not be able to post consistently until at least mid-June. The roadmap is as such, if I pass, I will start introductory lessons in Econometrics and Statistics (if not, then I'll have to study until I can retake the comps in August). I hope that once I am done, I will be able to add more advance materials to the blog, such as general equilibrium, indirect utility functions, and game theory/mechanism design for Micro. The Solow, Ramsey, RBC, New Keynesian models, permanent income hypothesis (PIH) and more for Macro. By the way I think I still need to add notes on the IS-LM curves, so I will do that before jumping to t...