Consider two equations describing the relationship between three variables X, Y1, and Y2: X = a b Y1, (1) X = c – d Y2, (2) where a, b, c, and d, are positive, known constants (numbers). The objective is to find values of X, Y1, and Y2 for which both equations are satisfied and as well Y1 = Y2. a. How many unknown variables are there? Clearly identify them. How many equations are there? Clearly identify them. Note that there should be as many equations as unknown variables. When this is the case, a unique solution exists. (Try to convince yourself that having only (1) and (2) Page 4 of 5 makes it impossible to solve for the unknown variables, by equating X from (1) to X from (2) and trying to solve for Y1 and Y2.) b. Replace both sides of the third equation (which one is it?) using expressions (1) and (2) to solve for X. c. After solving for X, find the values of Y1 and Y2 and verify whether the third equation is satisfied. d. Now, rename Y1 as Q S representing quantity supplied, replace a with 200, replace b with 2, rename Y2 as Q D representing quantity supplied, replace c with 400, replace d with 3, and rename X as P representing price. This gives you a system of supply and demand for a good. Re-write expressions (1) and (2) using this information. How many unknown variables and how many equations do you have? e. To find the equilibrium and solve for equilibrium values of Q D , Q S , and P, what other condition do we need? [Hint: Think about our discussion in class and the fill the blank here to find out what other condition you might need: “If quantity demanded is more than quantity supplied, the price will ________. If quantity demanded is less than quantity supplied, then price will _________. So, price will not change only if quantity demanded _________ quantity supplied. This is how we define equilibrium: a condition under which variables in the model remain stable and do not change. We call this additional equation market-clearing condition.”] f. Given the system of supply and demand and the market-cle