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Problem 5 Assume the market price of'coal is $6.4 per ton. At that price the consumption as well as production are 23 trillion tons, Also, the average price of crude oil is $50 per barrel. A reasonable estimate for the price elasticity of coal supplj,I is {t1 Due to the production technology;r higher oil prices lead to more coal production. Thus, the cross-price elasticity of supply is estimated to he Ill _ The price elasticity of demand for coal is -.5, while the cross- price elasticity with respect to oil price is L5. a. Find the demand curve for coal (Hint: Compute parameters a, a, and e in er= a chmt+ aPmr) 11. Find the supply' curve for coal (Hint: |Compute parameters a, d, and g in QC\"; = c + chm: + gPa'] c. Verify that if the price of oil is $50, these curves imply a free-market price of$d.4 for coal. d. Suppose the government determines that the free market price of ad for coal is too high, and decides to control the price by setting a maximum price of $3. What would he the impact on the quantity ot'coal supplied and demanded?I c. Now suppose the regulated price of coal were $45!} per ton instead of $3.00. How much excess demand would there have been? f. Suppose that the market for coal remained turregulated, If'the price ofoil had increased from t} to $t DD, what would have happened to the free-market price of coal